Speech and Language Processing Lecture 2 Chapter 2 of SLP
Today • Finite-state methods Speech and Language Processing - Jurafsky and Martin 7/29/08 2
Regular Expressions and Text Searching • Everybody does it Emacs, vi, perl, grep, etc.. • Regular expressions are a compact textual representation of a set of strings representing a language. Speech and Language Processing - Jurafsky and Martin 7/29/08 3
Example • Find all the instances of the word “the” in a text. /the/ /[tT]he/ /\b[tT]he\b/ Speech and Language Processing - Jurafsky and Martin 7/29/08 4
Errors • The process we just went through was based on two fixing kinds of errors Matching strings that we should not have matched (there, then, other) False positives (Type I) Not matching things that we should have matched (The) False negatives (Type II) Speech and Language Processing - Jurafsky and Martin 7/29/08 5
Errors • We’ll be telling the same story for many tasks, all semester. Reducing the error rate for an application often involves two antagonistic efforts: Increasing accuracy, or precision, (minimizing false positives) Increasing coverage, or recall, (minimizing false negatives). Speech and Language Processing - Jurafsky and Martin 7/29/08 6
Finite State Automata • Regular expressions can be viewed as a textual way of specifying the structure of finite-state automata. • FSAs and their probabilistic relatives are at the core of much of what we’ll be doing all semester. • They also capture significant aspects of what linguists say we need for morphology and parts of syntax. Speech and Language Processing - Jurafsky and Martin 7/29/08 7
FSAs as Graphs • Let’s start with the sheep language from Chapter 2 /baa+!/ Speech and Language Processing - Jurafsky and Martin 7/29/08 8
Sheep FSA • We can say the following things about this machine It has 5 states b, a, and ! are in its alphabet q 0 is the start state q 4 is an accept state It has 5 transitions Speech and Language Processing - Jurafsky and Martin 7/29/08 9
But Note • There are other machines that correspond to this same language • More on this one later Speech and Language Processing - Jurafsky and Martin 7/29/08 10
More Formally • You can specify an FSA by enumerating the following things. The set of states: Q A finite alphabet: Σ A start state A set of accept/final states A transition function that maps Qx Σ to Q Speech and Language Processing - Jurafsky and Martin 7/29/08 11
About Alphabets • Don’t take term alphabet word too narrowly; it just means we need a finite set of symbols in the input. • These symbols can and will stand for bigger objects that can have internal structure. Speech and Language Processing - Jurafsky and Martin 7/29/08 12
Dollars and Cents Speech and Language Processing - Jurafsky and Martin 7/29/08 13
Yet Another View • The guts of FSAs b a ! e can ultimately be 0 1 represented as 1 2 tables 2 2,3 If you’re in state 1 3 4 and you’re looking at an a, go to state 2 4 Speech and Language Processing - Jurafsky and Martin 7/29/08 14
Recognition • Recognition is the process of determining if a string should be accepted by a machine • Or… it’s the process of determining if a string is in the language we’re defining with the machine • Or… it’s the process of determining if a regular expression matches a string • Those all amount the same thing in the end Speech and Language Processing - Jurafsky and Martin 7/29/08 15
Recognition • Traditionally, (Turing’s notion) this process is depicted with a tape. Speech and Language Processing - Jurafsky and Martin 7/29/08 16
Recognition • Simply a process of starting in the start state • Examining the current input • Consulting the table • Going to a new state and updating the tape pointer. • Until you run out of tape. Speech and Language Processing - Jurafsky and Martin 7/29/08 17
D-Recognize Speech and Language Processing - Jurafsky and Martin 7/29/08 18
Key Points • Deterministic means that at each point in processing there is always one unique thing to do (no choices). • D-recognize is a simple table-driven interpreter • The algorithm is universal for all unambiguous regular languages. To change the machine, you simply change the table. Speech and Language Processing - Jurafsky and Martin 7/29/08 19
Key Points • Crudely therefore… matching strings with regular expressions (ala Perl, grep, etc.) is a matter of translating the regular expression into a machine (a table) and passing the table and the string to an interpreter Speech and Language Processing - Jurafsky and Martin 7/29/08 20
Recognition as Search • You can view this algorithm as a trivial kind of state-space search . • States are pairings of tape positions and state numbers. • Operators are compiled into the table • Goal state is a pairing with the end of tape position and a final accept state • It is trivial because? Speech and Language Processing - Jurafsky and Martin 7/29/08 21
Generative Formalisms • Formal Languages are sets of strings composed of symbols from a finite set of symbols. • Finite-state automata define formal languages (without having to enumerate all the strings in the language) • The term Generative is based on the view that you can run the machine as a generator to get strings from the language. Speech and Language Processing - Jurafsky and Martin 7/29/08 22
Generative Formalisms • FSAs can be viewed from two perspectives: Acceptors that can tell you if a string is in the language Generators to produce all and only the strings in the language Speech and Language Processing - Jurafsky and Martin 7/29/08 23
Non-Determinism Speech and Language Processing - Jurafsky and Martin 7/29/08 24
Non-Determinism cont. • Yet another technique Epsilon transitions Key point: these transitions do not examine or advance the tape during recognition Speech and Language Processing - Jurafsky and Martin 7/29/08 25
Equivalence • Non-deterministic machines can be converted to deterministic ones with a fairly simple construction • That means that they have the same power; non-deterministic machines are not more powerful than deterministic ones in terms of the languages they can accept Speech and Language Processing - Jurafsky and Martin 7/29/08 26
ND Recognition Two basic approaches (used in all major • implementations of regular expressions, see Friedl 2006) 1. Either take a ND machine and convert it to a D machine and then do recognition with that. 2. Or explicitly manage the process of recognition as a state-space search (leaving the machine as is). Speech and Language Processing - Jurafsky and Martin 7/29/08 27
Non-Deterministic Recognition: Search • In a ND FSA there exists at least one path through the machine for a string that is in the language defined by the machine. • But not all paths directed through the machine for an accept string lead to an accept state. • No paths through the machine lead to an accept state for a string not in the language. Speech and Language Processing - Jurafsky and Martin 7/29/08 28
Non-Deterministic Recognition • So success in non-deterministic recognition occurs when a path is found through the machine that ends in an accept. • Failure occurs when all of the possible paths for a given string lead to failure. Speech and Language Processing - Jurafsky and Martin 7/29/08 29
Example b a a a ! \ q 0 q 2 q 1 q 2 q 3 q 4 Speech and Language Processing - Jurafsky and Martin 7/29/08 30
Example Speech and Language Processing - Jurafsky and Martin 7/29/08 31
Example Speech and Language Processing - Jurafsky and Martin 7/29/08 32
Example Speech and Language Processing - Jurafsky and Martin 7/29/08 33
Example Speech and Language Processing - Jurafsky and Martin 7/29/08 34
Example Speech and Language Processing - Jurafsky and Martin 7/29/08 35
Example Speech and Language Processing - Jurafsky and Martin 7/29/08 36
Example Speech and Language Processing - Jurafsky and Martin 7/29/08 37
Example Speech and Language Processing - Jurafsky and Martin 7/29/08 38
Key Points • States in the search space are pairings of tape positions and states in the machine. • By keeping track of as yet unexplored states, a recognizer can systematically explore all the paths through the machine given an input. Speech and Language Processing - Jurafsky and Martin 7/29/08 39
Why Bother? • Non-determinism doesn’t get us more formal power and it causes headaches so why bother? More natural (understandable) solutions Speech and Language Processing - Jurafsky and Martin 7/29/08 40
Compositional Machines • Formal languages are just sets of strings • Therefore, we can talk about various set operations (intersection, union, concatenation) • This turns out to be a useful exercise Speech and Language Processing - Jurafsky and Martin 7/29/08 41
Union Speech and Language Processing - Jurafsky and Martin 7/29/08 42
Recommend
More recommend
